Assume Judy hates chocolate but likes vanilla and strawberry the same. She decides therefore to make one portion with 6 oz chocolate and 12 oz vanilla, with the other portion being 6 oz chocolate and 12 oz strawberry. Thus no matter what Sam picks, Judy can get stuck with at most half of the chocolate. Assume Sam hates chocolate and vanilla but loves strawberry. Thus Sam leaves Judy the vanilla-chocolate portion and keeps the strawberry-chocolate portion. Judy now cuts her portion into three pieces. She cuts the vanilla into three equal pieces and puts the chocolate with one of those pieces. Thus the three pieces are: a 4 oz portion of vanilla, another 4 oz portion of vanilla, and a third portion which is 4 oz vanilla plus 6 oz chocolate. Sam divides his portion into: a 4 oz portion of strawberry, another 4 oz portion of strawberry, and a third portion which is 4 oz strawberry plus 6 oz chocolate.